New stochastic linear programming approximations for network capacity control problem with buy-ups

It is well known that the network capacity control problem can be formulated as a dynamic programming model. However, this formulation is intractable in practice due to its size and complexity. As a result various approximation methods are proposed in the literature. Decomposition and deterministic linear programming approximations are formulated and have been successfully used in practice. Lately, several stochastic programming (SP) approaches that take demand uncertainty into account have been published. This paper adds to recent research on SP methodologies by considering the customer's buy-up behaviour. We provide three new formulations based on different sets of assumptions. Then, we simulate demand arrival processes under four different simulation scenarios to compare the performance of each model with deterministic and randomised linear programming approximations.